Answers
Answer:
The correct answer is 12/37
Related Questions
A homebuyer is building a home and has sat down with an architect. The buyer tells the architect the perimeter of the house must be 200
feet. The dimensions of the house that would give the buyer the maximum area would be which of the following?
A 10 x 90 feet
B 20 x 80 feet
C 30 x 70 feet
40 x 60 feet
E 50 x 50 feet
Answers
Answer:
[tex]50\; {\rm ft} \times 50\; {\rm ft}[/tex] would maximize the area for a rectangle with the given circumference of [tex]200\; {\rm ft}[/tex]. (Note, that a circle of the same circumference would have an even larger area.)
Step-by-step explanation:
Assume that the base of the house is a rectangle. Let the length of the two sides be [tex]x\; {\rm ft}[/tex] and [tex]y\; {\rm ft}[/tex], respectively. The goal is to find the [tex]x[/tex] and [tex]y[/tex] that:
[tex]\begin{aligned} \text{maximize} \quad & x\, y \\ \text{subject to} \quad & 2\, (x + y) = 200 \\ & x > 0 \\ & y > 0 \end{aligned}[/tex].
Using the equality constraint [tex]2\, (x + y) = 200[/tex] (or [tex]x + y = 100[/tex]), the variable [tex]y[/tex] could be replaced with [tex](100 - x)[/tex] to obtain an equivalent problem of only one variable:
[tex]\begin{aligned} \text{maximize} \quad & x\, (100 - x) \\ \text{subject to} \quad & x > 0 \\ & (100 - x) > 0 \end{aligned}[/tex].
Simplify to obtain:
[tex]\begin{aligned} \text{maximize} \quad & -x^{2} + 100\, x \\ \text{subject to} \quad & x > 0 \\ & x < 100 \end{aligned}[/tex].
The objective function of this problem is [tex]f(x) = -x^{2} + 100\, x[/tex]. Derivatives of this function include
[tex]f^{\prime}(x) = -2\, x + 100[/tex] and[tex]f^{\prime\prime}(x) = -2[/tex].Since [tex]f^{\prime\prime}(x)[/tex] is constantly less than [tex]0[/tex], [tex]f(x)[/tex] is concave and would be maximized when [tex]f^{\prime}(x) = 0[/tex].
Setting [tex]f^{\prime}(x) = -2\, x + 100[/tex] to [tex]0[/tex] and solving for [tex]x[/tex] gives:
[tex]-2\, x + 100 = 0[/tex].
[tex]x = 50[/tex].
Notice that [tex]x = 50[/tex] satisfies both constraints: [tex]x > 0[/tex] and [tex]x < 100[/tex]. Therefore, [tex]x = 50[/tex] is indeed the solution that maximizes the area [tex]f(x) = -x^{2} + 100\, x[/tex] while at the same time meeting the requirements.
With the length of one side being [tex]x = 50[/tex] ([tex]50\; {\rm ft}[/tex],) the length of the other side would be [tex]100 - x = 50[/tex] ([tex]50\; {\rm ft}\![/tex].) Hence, a rectangular house of dimensions [tex]50\; {\rm ft} \times 50\; {\rm ft}[/tex] would maximize the area under the given requirements.
Richard owns a restaurant. He needs to buy at least 300 glasses. Tall glasses cost $2.50. Short glasses
cost $2.10. He can spend at most $670. Which system of inequalities can Richard use to find the possible
numbers of tall glasses, I, and short glasses, s, he can buy?
Answers
Answer:
l+s≥300
2.5l+2.1s≤670
Step-by-step explanation:
please help me find the answer
Answers
Answer:
the angle is equal to 60 degree
Which expression is equivalent to 4(2n) + n?
A : 8n
B : 9n
C : 6n + n
D : 8n + n
Answers
Answer:
B and D.
Step-by-step explanation:
4(2n) + n
= 8n + n
= 9n.
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
[tex] \large\underline{ \boxed{ \sf{✟\:Important\: point's✟ }}}[/tex]
we can easily check whether the given expression is equivalent or not by simply solving the expression by fôllowling algebraic rule→ Your given expression:- 4(2n)+n
★ Let's solve:-➤4(2n)+n➤distributing 4 with 2n gives you ➤8n+n➤then adding like terms➤9n☆ Hence option b (9n) is right ans
[tex]\pink{\underline{ \underline{ \boxed{ \sf{✰\: Option.\:B✓ }}}}}[/tex]
Hope it helps !
You deposit all of your graduation money, $2,560, into an account earning 3.5% interest, compounded annually. You want to let it sit, no deposits or withdraws, while you are in college for 4 years. How much will you have at the end of 4 years? Round to the nearest cent.
Answers
Answer:
To calculate compounded interest, use the compound interest formula.
A(t)=P(1+rn)n⋅t
Recognize the information given in the problem.
P=2560,r=0.035,n=1,t=4
Substitute the values into the appropriate position in the formula.
A(4)=2560(1+0.0351)1⋅4
Simplify by multiplying and dividing by 1.
A(4)=2560(1+0.035)4
Simplify using the order of operations.
A(4)=$2,937.66
The balance at the end of 4 years would be $2,937.66.
Step-by-step explanation:
Find the area of the figure.
Answers
Answer:
[tex]\huge\boxed{\sf 9300\ m\²}[/tex]
Step-by-step explanation:
The figure is made up of:
A rectangle A triangleFormula for area of rectangle:
Length × WidthFormula for Area of triangle:
[tex]\displaystyle =\frac{1}{2} (Base)(Height)[/tex]Area of rectangle:
Length = 90 m
Width = 70 m
= Length × Width
= 90 × 70
= 6300 m²
Area of Triangle:
Base = 170 - 70 = 100 m
Height = 90 - 30 = 60 m
[tex]\displaystyle =\frac{1}{2} (Base)(Height)\\\\= \frac{1}{2} (100)(60)\\\\= (50)(60)\\\\= 3000 \ m^2[/tex]
Total Area of the figure:
= Area of the rectangle + Area of the triangle
= 6300 + 3000
= 9300 m²
[tex]\rule[225]{225}{2}[/tex]
solve the following absolute value
Answers
Answer:
x < 2
Step-by-step explanation:
|-7x+4| < 18
7x + 4 < 18
7x + 4 - 4 < 18 - 4
7x < 14
7x/7 < 14/7
x < 2
im not sure if this is right but this is what i got.
Suppose the dimensions of a rectangle with a perimeter of 18 inches are quadrupled. Find the perimeter of the new rectangle in inches
Answers
The new perimeter of the rectangle if the dimensions are quadrupled would be 72 inches.
What are the side lengths of the first triangle?The perimeter is always obtained by adding all the sides. This means the possible side lengths of the original rectangle are:
5 inches + 5 inches + 4 inches + 4 inchesWhat are the side lengths of the new triangle?5 inches x 4 = 20 inches
4 iches x 4 = 16 inches
What is the new perimeter?20 + 20 + 16 +16= =72 inches
Learn more about perimeter in: https://brainly.com/question/6465134
2/5+3/8 5th grade Math. Please help.
Answers
Answer:
31/40
Step-by-step explanation:
Given expression:
[tex]\dfrac{2}{5} + \dfrac{3}{8}[/tex]
Note: Both fractions must have same denominators if we want to perform addition, subtraction, multiplication, or division.
The only way to simplify this expression is to have a common denominator, which can be determined by the LCM of 5 and 8.
⇒ Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45...⇒ Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72...Multiply the denominators with such a number that is equivalent to 40.
Note: The number you are multiplying should also be multiplied to the numerator.
[tex]\rightarrow \dfrac{2 \times 8}{5 \times 8} + \dfrac{3 \times 5}{8 \times 5}[/tex]
[tex]\rightarrow \dfrac{16}{40} + \dfrac{15}{40}[/tex]
Finally, simplify the expression to determine the solution.
[tex]\rightarrow \dfrac{31}{40}[/tex]
Since 31 is a prime number, we can't simplify this fraction. Thus, the final answer is 31/40.
Ah yes, adding fractions! Adding fractions can be a bit of a pain.
So, we have [tex]\frac{2}{5} + \frac{3}{8}[/tex].
To add fractions, the bottoms, or denominators, must be the same number. So we must multiply the fractions by certain numbers to make the denominators the same number. So let's go easy and make the denominator 40, because 8 goes into 40 and so does 5. So, to make 8 become 40, we'll multiply the whole fraction by 5. For 5, we'll multiply by 8.
[tex]5 * \frac{3}{8} = \frac{15}{40}[/tex]
[tex]8 * \frac{2}{5} = \frac{16}{40}[/tex]
Now we'll add the two fractions. When we add fractions we only add the tops, the numerators.
[tex]\frac{15}{40}+\frac{16}{40} = \frac{31}{40}[/tex]
Then we must reduce (or try to reduce). This fraction cannot be reduced, so the answer is simply [tex]\frac{31}{40}[/tex].
I hope this helps you understand.
-Toremi
Calculate the distance between the points G=(-2, 2) and C = (5, -1) in the coordinate plane.
=
Give an exact answer (not a decimal approximation).
Answers
Answer: sqrt(58)
Step-by-step explanation:
if sid has 15 mangoes and sera has 6 apples , what is the total number of fruits with sidra ?
[tex] \\ \\ \\ [/tex]
thankyou ~
Answers
[tex] \huge \mathfrak \red{HeY \: ThErE♡}[/tex]
Given,No. of mangoes sid has = 15
No. of apples sera has = 6
Therefore, we gonna add them-,-Total no. of fruits Sidra will have = 15 + 6 = 21
Therefore,Sidra will have 21 fruits.[tex] \huge \mathfrak \red{HoPe \: It \: HeLpS♤}[/tex]
1. Children must be at most 36 inches tall to ride the kiddie roller
coaster. Let h = the height required to ride the kiddie roller coaster.
2. The gym can seat a maximum of 1200 people.
Let n = the number of people who can sit in the gym.
3. Children must be at least 13 to go to a PG-13 rated movie.
Let a = the age you must be to attend a PG-13 movie.
Answers
Answer:
Step-by-step explanation:
1.) H (greater than or equal to) 36in
2.) N (Less than or equal to) 1200
3.) A (greater than or equal to) 13
A camera has a listed price of 643.99 before tax. If the sales tax rate is 9.75%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answers
Answer: $1,271.88
Step-by-step explanation:
The total cost of the camera with sales tax included will be 100% plus our sales tax:
100% + 9.75% = 109.75%
Dividing a percent (%) by 100 gives us a decimal:
109.75% / 100 = 1.975
We can multiply this decimal by the listed price of the camera to find our answer
643.99 * 1.975 = $1,271.88
The camera will cost $1,271.88 with sales tax.
50 POINTS NO LINKS
An object is launched at 39.2 meters per second (m/s) from a 42.3-meter tall platform. The equation for the objects height s at time t seconds after launch is s(t)=-4.9t^2+39.2t+42.3, where s is in meters. Create a table of values and graph the function. Approximately what is the maximum height of the object?
Answers
Convert into vertex form y=a(x-h)²+k
y=-4.9t²+39.2t+42.3After calculating
y=-4.9(x-39.2)²+42.3Vertex at
(39.2,42.3)Max height=42.3m
Graph attached
Use the expression 4(8 + 3x) to answer the following: Part A: Describe the two factors in this expression. (4 points) Part B: How many terms are in each factor of this expression? (4 points) Part C: What is the coefficient of the variable term? (2 points)
Answers
Given : 4(8 + 3x)
To Find : Describe the two factors in this expression
How many terms are in each factor of this expression
coefficient of the variable term
Solution:
4(8 + 3x)
two factors in this expression are
4 and ( 8 + 3x)
terms in each factor of this expression
1 term in 4
2 terms in (8 + 3x)
coefficient of the variable term is 3 in factorized form
4(8 + 3x) = 32 + 12x
and coefficient of the variable term is 12 in expanded form
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find the value of x by factorization, x2-8x+1280=0 - Brainly.in
https://brainly.in/question/7343350
Using factor theorem, factorize each of the following polynomial ...
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Factorise: 1. a3 – 4a2 + 12 – 3a 2. a3x – x4 + a2x2
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A coin is flipped 8 times. Find the probability of the event: exactly 5 heads a. 0.625 b. 0.03125 c. 0.219 d. 0.0039
Answers
The probability of the event of getting exactly 5 heads in 8 tosses of a coin(assuming unbiased coin) is given by: Option C: 0.219 (approximately).
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]
For this case, we've got:
A coin is flipped 8 times.To find: P(getting exactly 5 heads)Each coin flip is a bernoulli distribution as it has two possible outcomes (assuming any other outcome like coin landing standing straight etc ignored). Take success = getting head in a flip, and failure = not getting success= not getting head = getting tail as the outcome of the flip.
Now, each of those 8 flips are independent in terms of result of each other (assuming coin stays unbiased).
If we take:
X = number of heads out of those 8 flips = number of successes in those 8 bernoulli trials, then:
[tex]X \sim B(n = 8, p)[/tex]
where p is the probability of success = P(Getting head in an unbiased coin with head or tail as only possible outcomes) = 1/2 = 0.5 (as head can come in 1 way, and total outcomes is 2, all equally likely).
Thus, we get:
[tex]X \sim B(n = 8, p=0.5)[/tex]
Now, P(Exactly 5 heads in those 8 flips) = P(X = 5)
Using the probability function of the binomial distribution, we get:
[tex]P(X = 5) = \: ^8C_5(0.5)^5(0.5)^{8-5} = \dfrac{8\times 7\times 6\times 5\times 4}{5 \times 4 \times 3\times 2 \times 1} \times (0.5)^8 \approx 0.219[/tex]
Thus, the probability of the event of getting exactly 5 heads in 8 tosses of a coin(assuming unbiased coin) is given by: Option C: 0.219 (approximately).
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Year Speed 1 38 2 46 3 52 4 57 5 61 3) During which time period was the ANNUAL rate of increase of the speed the GREATEST? HELP FAST
A) from year 1 to year 2
B) from year 1 to year 3
C) from year 1 to year 4
D) from year 1 to year 5
Answers
Answer: A) from year 1 to year 2
Step-by-step explanation: subtract 46-38=8, I also just took the K12 test and got it right.
Answer:
A) from year 1 to year 2
Step-by-step explanation:
x= -1/8y2
The focus of the parabola is:
O (0, -2)
O (2, 0)
O (-2, 0)
Answers
x=-1/8y²
Interchange x and y
y=-1/8x²Compare to Vertex form y=a(x-h)²+k
a=-1/8Now
1/4a1/4(-1/8)-2.So
Focus (-2,0)
Answer:
(-2, 0)
Step-by-step explanation:
Standard form of a parabola with a horizontal axis of symmetry:
[tex](y-k)^2=4p(x-h)\quad \textsf{where}\:p\neq 0[/tex]
[tex]\textsf{Vertex}=(h, k)[/tex]
[tex]\textsf{Focus}=(h+p,k)[/tex]
Given equation:
[tex]x=-\dfrac18y^2[/tex]
Rewrite in standard form:
[tex]\implies (x-0)=-\dfrac18(y-0)^2[/tex]
[tex]\implies -8(x-0)=(y-0)^2[/tex]
[tex]\implies (y-0)^2=-8(x-0)[/tex]
Comparing with the general standard form:
k = 0h = 04p = -8 ⇒ p = -2Therefore:
[tex]\textsf{Vertex }(h,k)=(0,0)[/tex]
[tex]\textsf{Focus }(h+p,k)=(0-2,0)=(-2,0)[/tex]
estimate 259+372 by rounding each number to the nearest 10
Answers
Answer: ok well the answer is 631 if it were rounded it would be 630
Now if u mean those 2 numbers they would be 259:260 and 372:370 there hope it helps bye!
Please help I'll mark brainliest
Answers
Answer:
The godsStep-by-step explanation:
Heroes in Greek Mythology were men or women of special strength, courage, or ability. They were often of divine ancestry and noted for superhuman courageous acts.
What makes a hero in Greek Mythology?
Having one immortal parent. Being born into royalty. Having an unusual conception or birth. Being favored by the gods. Being the subject of a prophesy. Being abandoned at birth or while very young. Performing an amazing feat at a young age. Going on a quest.The table of values represents a continuous function. Which type of function describes g(x)?
Rational
Polynomial
Logarithmic
Exponential
Answers
A logarithimic function is a function of the sort; loga(a^x) = x. The function that is described by g(x) is a logarithmic function.
What is a lograithimic function?A logarithimic function is a function of the sort; loga(a^x) = x. We now have to look at this table to ascertain of this condition is met.
Given this condition, we can see that each of the entries in the table satisfies this basic criterion of a logarithmic function hence, the function that is described by g(x) is a logarithmic function.
Learn more about logarithmic function: https://brainly.com/question/14356798
Answer:
Exponential
Step-by-step explanation:
The function g(x) described by the given table of values is most likely an exponential function because x increases by a constant factor and the values of g(x) increase or decrease by a consistent factor. This behavior aligns with the characteristics of an exponential function, where the variable x appears in the exponent. I put polynomial as my answer on the test and got it incorrect and then realized the answer was exponential.
What is the perimeter?
Answers
Answer:
i believe your answer is 41,
Step-by-step explanation:
because to find perimeter, you simply have to add up all of the sides unlike area where you have to multiply, giving you 18+18+2+2=41 for your answer
Answer:
41
Step-by-step explanation:
add up all the sides total to 41
A class is made up of 54% women and has 21 women in it. What is the total number of students in the class?
Answers
Answer:
39
Step-by-step explanation:
percentage=part/total x 100
54= 21 / total x 100
total=38.88 = 39
What is standard deviation?
Group of answer choices
The difference in the maximum and minimum valudes of the data set.
measure of how dispersed the data is in relation to the mean.
The difference in Quartile 3 and Quartile 1.
the center of the data
Answers
Answer:
The difference in Quartile 3 and Quartile 1.
A politician wants to estimate the proportion of constituents favouring a controversial piece of proposed legislation. Suppose that a 99% confidence interval that extends at most 0.05 on each side of the sample proportion is required. How many sample observations are needed?
Answers
Answer:
I pressed this by an accident
by selling an article for #2500 a trader made a profit of #200.find the percentage profit of the article.
Answers
Answer:
I'm going to assume the # is meant $, if that is the case then the trader made 8% profit
Step-by-step explanation:
200 out of 2500 is basically 200/2500. 200 divided by 2500 is 0.08, and to find the percent of a number you have to multiply it by ten (or just move the decimal two places to the right) 0.08 multiplied by 10 would give you 8, so the answer is 8 percent. Hope this helps!
Hii can you help me? 6/2(1+2)
I really stink at math :(
Answers
Answer:
6/2(1+2)
First lets simplify whats in the parentheses
6/2(3)
So thats 6/2 * 3
6/2 = 3
3*3 =
9
Answer:
9
Step-by-step explanation:
first, you do (1+2) which is 3 and then you do 6/2 which is 3 then 3x3 is 9
The Payans have just learned that the bank will approve them for a mortgage at an APR of 4.3% for 30 years if they meet the back-end ratio requirement. To determine whether they’ll meet the requirement, the back-end ratio needs to be calculated with the actually monthly payment rather than the estimate used in part A. Use this monthly payment formula to calculate the Payans’ monthly mortgage payment.
Answers
The annual percentage rate (APR) for the Payans is the yearly interest rate that's generated by a sum charged to borrowers.
What is APR?Your information is incomplete as the values aren't given. Therefore, an overview will be given. Here, the APR is the cost that one has to pay to borrow money and it's expressed as a percentage.
Also, the mortgage payment is made up of the principal and the interest payments. It's how one will pay back their home loan.
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Answer:
1237.18
Step-by-step explanation:
Please solve and show work!!! Need by tomorrow look at attached photo!!<44
Answers
Answer:
1.
First, I would solve for ACB.
Calculations:
63° = y?
I would do that because I know that angle 'y' is vertical to 63°, which is given. (Also vertical angles are congruent, meaning that the measure the same degrees).
2.
Second, I would solve for BAC.
Calculations:
x + 63 + 85 = 180
x + 148 = 180
-148 -148
x = 32°
I would do that because I know that there are two given angles so I could easily solve for the leftover angle, 'z', using the a + b + c = 180° formula.
3.
Next, I would solve for CED.
Calculations:
x + 130 = 180
-130 -130
x = 50°
I would do that because I know finding this angle will help me find angle CDE.
4.
Finally, I would solve for CDE.
Calculations:
x + 63 + 50 = 180
x + 113 = 180
-113 -113
x = 67°
I would do that because I know there are now two given angles so I could easily solve for the leftover angle, x, using the a + b + c = 180° formula.
can someone help with this please
Answers
Y=mx+b form:
y<2/5x+2
y ≥ -1/2x+3
I forgot how to do the inequalities :)
Step-by-step explanation: